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Proof step 196 from proof inv-unlink (previous step)

# links(entries0[str], dirs0) = m2 + 1, icache0[ino].inode = mkinode(m9, md4, boolvar1, m10, m11, m12), icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] = mkientry(boolvar0, mkinode(m, md, boolvar, m4, m5, m6)), files0[entries0[str]] = mkfile(m1, md1, m2 + 1, content0), dirs0[m0] = mkdir(m8 + 1, md2, # links(m0, dirs0), m7, entries0), afs-cons(dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]), afs-cons(dirs0, files0), synced(dirs0, icache0, pcache), m0 ∈ dirs0, entries0[str] ∈ files0, str ∈ entries0, ino ∈ icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ], asynced1 → synced(files0, icache0, pcache), ino ∈ icache0 → m9 = ino ∧ (icache0[ino].dirty ⊃ ino ∈ files0 ∧ m10 = files0[ino].nlink ∧ m11 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs0 ∨ ino ∈ files0) ∧ mkinode(ino, md4, boolvar1, m10, m11, m12) = (ino ∈ dirs0 ⊃ mkinode(ino, dirs0[ino].meta, true, dirs0[ino].nlink, dirs0[ino].nsubdirs, dirs0[ino].size) ;mkinode(ino, files0[ino].meta, false, files0[ino].nlink, 0, files0[ino].size) ) ), ∀ ino0. ino0 ∈ icache0 → icache0[ino0].inode.ino = ino0 ∧ (icache0[ino0].dirty ⊃ icache0[ino0].inode.ino ∈ files0 ∧ icache0[ino0].inode.nlink = files0[icache0[ino0].inode.ino].nlink ∧ icache0[ino0].inode.nsubdirs = 0 ∧ ¬ icache0[ino0].inode.directory ; (ino0 ∈ dirs0 ∨ ino0 ∈ files0) ∧ icache0[ino0].inode = (icache0[ino0].inode.ino ∈ dirs0 ⊃ mkinode (icache0[ino0].inode.ino, dirs0[icache0[ino0].inode.ino].meta, true, dirs0[icache0[ino0].inode.ino].nlink, dirs0[icache0[ino0].inode.ino].nsubdirs, dirs0[icache0[ino0].inode.ino].size) ;mkinode (icache0[ino0].inode.ino, files0[icache0[ino0].inode.ino].meta, false, files0[icache0[ino0].inode.ino].nlink, 0, files0[icache0[ino0].inode.ino].size) ) ), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ m = ino ∧ (boolvar0 ⊃ ino ∈ files0 ∧ m4 = (ino = entries0[str] ⊃ mkfile(m3, md0, m2, content0);files0[ino]).nlink ∧ m5 = 0 ∧ ¬ boolvar ; (ino ∈ dirs0 ∨ ino ∈ files0) ∧ mkinode(ino, md, boolvar, m4, m5, m6) = (ino ∈ dirs0 ⊃ mkinode (ino, (ino = m0 ⊃ mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str);dirs0[ino]).meta, true, (ino = m0 ⊃ mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str);dirs0[ino]).nlink, (ino = m0 ⊃ mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str);dirs0[ino]).nsubdirs, (ino = m0 ⊃ mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str);dirs0[ino]).size) ;mkinode (ino, (ino = entries0[str] ⊃ mkfile(m3, md0, m2, content0);files0[ino]).meta, false, (ino = entries0[str] ⊃ mkfile(m3, md0, m2, content0);files0[ino]).nlink, 0, (ino = entries0[str] ⊃ mkfile(m3, md0, m2, content0);files0[ino]).size) ) )

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 197:
# links(entries0[str], dirs0) = m2 + 1, dirs0[m0] = mkdir(m8 + 1, md2, # links(m0, dirs0), m7, entries0), files0[entries0[str]] = mkfile(m1, md1, m2 + 1, content0), icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] = mkientry(boolvar0, mkinode(m, md, boolvar, m4, m5, m6)), icache0[ino] = mkientry(boolvar2, inode), inode = mkinode(m9, md4, boolvar1, m10, m11, m12), afs-cons(dirs0, files0), afs-cons(dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]), synced(dirs0, icache0, pcache), ino ∈ icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ], str ∈ entries0, entries0[str] ∈ files0, m0 ∈ dirs0, ino ∈ icache0 → m9 = ino ∧ (boolvar2 ⊃ ino ∈ files0 ∧ m10 = files0[ino].nlink ∧ m11 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs0 ∨ ino ∈ files0) ∧ mkinode(ino, md4, boolvar1, m10, m11, m12) = (ino ∈ dirs0 ⊃ mkinode(ino, dirs0[ino].meta, true, dirs0[ino].nlink, dirs0[ino].nsubdirs, dirs0[ino].size) ;mkinode(ino, files0[ino].meta, false, files0[ino].nlink, 0, files0[ino].size) ) ), asynced1 → synced(files0, icache0, pcache), ∀ ino0. ino0 ∈ icache0 → icache0[ino0].inode.ino = ino0 ∧ (icache0[ino0].dirty ⊃ icache0[ino0].inode.ino ∈ files0 ∧ icache0[ino0].inode.nlink = files0[icache0[ino0].inode.ino].nlink ∧ icache0[ino0].inode.nsubdirs = 0 ∧ ¬ icache0[ino0].inode.directory ; (ino0 ∈ dirs0 ∨ ino0 ∈ files0) ∧ icache0[ino0].inode = (icache0[ino0].inode.ino ∈ dirs0 ⊃ mkinode (icache0[ino0].inode.ino, dirs0[icache0[ino0].inode.ino].meta, true, dirs0[icache0[ino0].inode.ino].nlink, dirs0[icache0[ino0].inode.ino].nsubdirs, dirs0[icache0[ino0].inode.ino].size) ;mkinode (icache0[ino0].inode.ino, files0[icache0[ino0].inode.ino].meta, false, files0[icache0[ino0].inode.ino].nlink, 0, files0[icache0[ino0].inode.ino].size) ) ), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ m = ino ∧ (boolvar0 ⊃ ino ∈ files0 ∧ m4 = (ino = entries0[str] ⊃ mkfile(m3, md0, m2, content0);files0[ino]).nlink ∧ m5 = 0 ∧ ¬ boolvar ; (ino ∈ dirs0 ∨ ino ∈ files0) ∧ mkinode(ino, md, boolvar, m4, m5, m6) = (ino ∈ dirs0 ⊃ mkinode (ino, (ino = m0 ⊃ mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str);dirs0[ino]).meta, true, (ino = m0 ⊃ mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str);dirs0[ino]).nlink, (ino = m0 ⊃ mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str);dirs0[ino]).nsubdirs, (ino = m0 ⊃ mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str);dirs0[ino]).size) ;mkinode (ino, (ino = entries0[str] ⊃ mkfile(m3, md0, m2, content0);files0[ino]).meta, false, (ino = entries0[str] ⊃ mkfile(m3, md0, m2, content0);files0[ino]).nlink, 0, (ino = entries0[str] ⊃ mkfile(m3, md0, m2, content0);files0[ino]).size) ) )

Rule argument

spec: icache-entry name: elim seq: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode) subst: [ie, boolvar, inode] → [icache0[ino], boolvar2, inode]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode); (elim) Used terms: icache0[ino], boolvar2, inode